the Wythoff sequence

The Wythoff sequence involves two special sequences of numbers derived from the Fibonacci-inspired "golden ratio." These sequences are constructed using a systematic process that creates two increasing lists of numbers, known as Wythoff 0 and Wythoff 1. The sequences are connected to a strategy game called Wythoff Nim, where players remove objects from two piles. The key idea is that these sequences generate all the positions where a player can make a perfect move, and they are closely linked to the mathematical properties of mathematical constants and the Fibonacci sequence. In essence, they are structured, infinite number sequences with elegant mathematical relationships.